Question

The perimeter of a rectangle is 38 units. The length is 13 units longer than the width. What are the dimensions of the rectangle?

A 18 by 5
B. 12 by 7
Oc is by a
0.16 by

Answer 1

D (Presumably)

16 by 3

Explanation:

The perimeter of a rectangle is the two lengths added with the two widths. In a formula, this is:

`P=2l+2w`

Where l is the length and w is the width.

We are told the length is 13 units longer than the width. In other words:

`l=w+13`

We also already know that the perimeter is 38 units. So, let's substitute P for 38 and l for (w+13) to solve for w:

`P=2l+2w\\38=2(w+13)+2w`

Distribute:

`38=2w+26+2w`

Combine like terms:

`38=4w+26`

Subtract 26 from both sides:

`12=4w`

Divide both sides by 4:

`w=3`

Thus, the width is 3 units.

Since the length is 13 units longer than the width, the length is 16 units.